Problem: You are given an unweighted tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

Your task is to choose three distinct vertices a, b, c on this tree such that the number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c is the maximum possible. See the notes section for a better understanding.

The simple path is the path that visits each vertex at most once.

Input

The first line contains one integer number n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree. 

Next n - 1 lines describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). It is guaranteed that given graph is a tree.

Output

In the first line print one integer res — the maximum number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c.

In the second line print three integers a, b, c such that 1 ≤ a, b, c ≤ n and a ≠, b ≠ c, a ≠ c.

If there are several answers, you can print any.

Example

Input


8
1 2
2 3
3 4
4 5
4 6
3 7
3 8


Output


5
1 8 6

Note

The picture corresponding to the first example (and another one correct answer):

<image>

If you choose vertices 1, 5, 6 then the path between 1 and 5 consists of edges (1, 2), (2, 3), (3, 4), (4, 5), the path between 1 and 6 consists of edges (1, 2), (2, 3), (3, 4), (4, 6) and the path between 5 and 6 consists of edges (4, 5), (4, 6). The union of these paths is (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) so the answer is 5. It can be shown that there is no better answer.

Solution (in JAVA):

Solution:
/*
    Author: Anthony Ngene
    Created: 01/10/2020 - 18:10
*/

import java.io.*;
import java.util.*;

public class F {
// checks: 1. edge cases   2. overflow   3. possible errors (e.g 1/0, arr[out])   4. time/space complexity
    void solver() throws IOException {
        int n = in.intNext();
        Node[] nodes = adjacencyList(n, n - 1);
        bfs(nodes[1], nodes);
        end1 = furthest;
        bfs(furthest, nodes);
        end2 = furthest;
        int diameter = end2.dist;
        end2.inpath = true;
        dfsInPath(end1);
        for (int i = 1; i < n + 1; i++) if (nodes[i].inpath) dfsDept(nodes[i], 0);
        out.println(diameter + last.dist);
        out.pp(end1.val, end2.val, last.val);
    }

    Node last;
    void dfsDept(Node node, int dist) {
        node.visited = true;
        node.dist = dist;
        if (dist > last.dist) last = node;
        for (Node child : node.adj) {
            if (!child.visited && !child.inpath) dfsDept(child, 1 + dist);
        }
    }

    boolean dfsInPath(Node node) {
        node.dist = 0;
        if (last == null && !node.equals(end2) && !node.equals(end1)) last = node;
        if (node.equals(end2)) return true;
        node.visited = true;
        boolean inPath = false;
        for (Node child : node.adj) {
            if (!child.visited) {
                inPath |= dfsInPath(child);
            }
        }
        node.inpath = inPath;
        node.visited = false;
        return inPath;
    }

    Node furthest;
    Node end1;
    Node end2;
    void bfs(Node start, Node[] nodes) {
        for (int i = 1; i < nodes.length; i++) nodes[i].dist = -1;
        Deque<Node> deque = new ArrayDeque<>();
        start.dist = 0;
        furthest = start;
        deque.addLast(start);
        while (!deque.isEmpty()) {
            Node node = deque.pollFirst();
            for (Node child : node.adj) {
                if (child.dist == -1) {
                    child.dist = node.dist + 1;
                    deque.addLast(child);
                    if (child.dist > furthest.dist) furthest = child;
                }
            }
        }
    }

    class Node {
        List<Node> adj = new ArrayList<>();
        int val;
        int dist;
        boolean visited = false;
        boolean inpath = false;
        Node(int val) {
            this.val = val;
        }
        public void add(Node child) {
            adj.add(child);
        }
        @Override
        public String toString() {
            String res = val + ": " + dist + " " + inpath + ",";
            return res;
        }
    }
    public Node[] getAdj(int n) {
        Node[] adj = new Node[n + 1];
        for (int i = 1; i <= n; i++) adj[i] = new Node(i);
        return adj;
    }
    public Node[] adjacencyList(int nodes, int edges) throws IOException {
        return adjacencyList(nodes, edges, false);
    }
    public Node[] adjacencyList(int nodes, int edges, boolean isDirected) throws IOException {
        Node[] adj = getAdj(nodes);
        for (int i = 0; i < edges; i++) {
            int a = in.intNext(), b = in.intNext();
            adj[a].add(adj[b]);
            if (!isDirected) adj[b].add(adj[a]);
        }
        return adj;
    }
// Generated Code Below:
private static final FastWriter out = new FastWriter();
private static FastScanner in;
static ArrayList<Integer>[] adj;
private static long e97 = (long)1e9 + 7;
public static void main(String[] args) throws IOException {
    in = new FastScanner();
    new F().solver();
    out.close();
}

static class FastWriter {
    private static final int IO_BUFFERS = 128 * 1024;
    private final StringBuilder out;
    public FastWriter() { out = new StringBuilder(IO_BUFFERS); }
    public FastWriter p(Object object) { out.append(object); return this; }
    public FastWriter p(String format, Object... args) { out.append(String.format(format, args)); return this; }
    public FastWriter pp(Object... args) { for (Object ob : args) { out.append(ob).append(" ");  } out.append("\n"); return this; }
    public FastWriter pp(int[] args) { for (int ob : args) { out.append(ob).append(" ");  } out.append("\n"); return this; }
    public FastWriter pp(long[] args) { for (long ob : args) { out.append(ob).append(" ");  } out.append("\n"); return this; }
    public FastWriter pp(char[] args) { for (char ob : args) { out.append(ob).append(" ");  } out.append("\n"); return this; }
    public void println(long[] arr) { for(long e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(int[] arr) { for(int e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(char[] arr) { for(char e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(double[] arr) { for(double e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(boolean[] arr) { for(boolean e: arr) out.append(e).append(" "); out.append("\n"); }
    public <T>void println(T[] arr) { for(T e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(long[][] arr) {  for (long[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public void println(int[][] arr) {  for (int[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public void println(char[][] arr) {  for (char[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public void println(double[][] arr) {  for (double[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public <T>void println(T[][] arr) {  for (T[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public FastWriter println(Object object) { out.append(object).append("\n"); return this; }
    public void toFile(String fileName) throws IOException {
        BufferedWriter writer = new BufferedWriter(new FileWriter(fileName));
        writer.write(out.toString());
        writer.close();
    }
    public void close() throws IOException { System.out.print(out); }
}
static class FastScanner {
    private InputStream sin = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(){}
    public FastScanner(String filename) throws FileNotFoundException {
        File file = new File(filename);
        sin = new FileInputStream(file);
    }
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = sin.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long longNext() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b) || b == ':'){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int intNext() {
        long nl = longNext();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double doubleNext() { return Double.parseDouble(next());}
    public long[] nextLongArray(final int n){
        final long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = longNext();
        return a;
    }
    public int[] nextIntArray(final int n){
        final int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = intNext();
        return a;
    }
    public double[] nextDoubleArray(final int n){
        final double[] a = new double[n];
        for (int i = 0; i < n; i++)
            a[i] = doubleNext();
        return a;
    }
    public ArrayList<Integer>[] getAdj(int n) {
        ArrayList<Integer>[] adj = new ArrayList[n + 1];
        for (int i = 1; i <= n; i++) adj[i] = new ArrayList<>();
        return adj;
    }
    public ArrayList<Integer>[] adjacencyList(int nodes, int edges) throws IOException {
        return adjacencyList(nodes, edges, false);
    }
    public ArrayList<Integer>[] adjacencyList(int nodes, int edges, boolean isDirected) throws IOException {
        adj = getAdj(nodes);
        for (int i = 0; i < edges; i++) {
            int a = intNext(), b = intNext();
            adj[a].add(b);
            if (!isDirected) adj[b].add(a);
        }
        return adj;
    }
}
static class u {
    public static int upperBound(long[] array, long obj) {
        int l = 0, r = array.length - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj < array[c]) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }
    public static int upperBound(ArrayList<Long> array, long obj) {
        int l = 0, r = array.size() - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj < array.get(c)) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }
    public static int lowerBound(long[] array, long obj) {
        int l = 0, r = array.length - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj <= array[c]) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }
    public static int lowerBound(ArrayList<Long> array, long obj) {
        int l = 0, r = array.size() - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj <= array.get(c)) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }
    static <T> T[][] deepCopy(T[][] matrix) { return Arrays.stream(matrix).map(el -> el.clone()).toArray($ -> matrix.clone()); }
    static int[][] deepCopy(int[][] matrix) { return Arrays.stream(matrix).map(int[]::clone).toArray($ -> matrix.clone()); }
    static long[][] deepCopy(long[][] matrix) { return Arrays.stream(matrix).map(long[]::clone).toArray($ -> matrix.clone()); }
    private static void sort(int[][] arr){ Arrays.sort(arr, Comparator.comparingDouble(o -> o[0])); }
    private static void sort(long[][] arr){ Arrays.sort(arr, Comparator.comparingDouble(o -> o[0])); }
    private static <T>void rSort(T[] arr) { Arrays.sort(arr, Collections.reverseOrder()); }
    private static void customSort(int[][] arr) {
        Arrays.sort(arr, new Comparator<int[]>() {
            public int compare(int[] a, int[] b) {
                if (a[0] == b[0]) return Integer.compare(a[1], b[1]);
                return Integer.compare(a[0], b[0]);
            }
        });
    }
    public static int[] swap(int[] arr, int left, int right) {
        int temp = arr[left];
        arr[left] = arr[right];
        arr[right] = temp;
        return arr;
    }
    public static char[] swap(char[] arr, int left, int right) {
        char temp = arr[left];
        arr[left] = arr[right];
        arr[right] = temp;
        return arr;
    }
    public static int[] reverse(int[] arr, int left, int right) {
        while (left < right) {
            int temp = arr[left];
            arr[left++] = arr[right];
            arr[right--] = temp;
        }
        return arr;
    }
    public static boolean findNextPermutation(int[] data) {
        if (data.length <= 1) return false;
        int last = data.length - 2;
        while (last >= 0) {
            if (data[last] < data[last + 1]) break;
            last--;
        }
        if (last < 0) return false;
        int nextGreater = data.length - 1;
        for (int i = data.length - 1; i > last; i--) {
            if (data[i] > data[last]) {
                nextGreater = i;
                break;
            }
        }
        data = swap(data, nextGreater, last);
        data = reverse(data, last + 1, data.length - 1);
        return true;
    }
    public static int biSearch(int[] dt, int target){
        int left=0, right=dt.length-1;
        int mid=-1;
        while(left<=right){
            mid = (right+left)/2;
            if(dt[mid] == target) return mid;
            if(dt[mid] < target) left=mid+1;
            else right=mid-1;
        }
        return -1;
    }
    public static int biSearchMax(long[] dt, long target){
        int left=-1, right=dt.length;
        int mid=-1;

        while((right-left)>1){
            mid = left + (right-left)/2;
            if(dt[mid] <= target) left=mid;
            else right=mid;
        }
        return left;
    }
    public static int biSearchMaxAL(ArrayList<Integer> dt, long target){
        int left=-1, right=dt.size();
        int mid=-1;

        while((right-left)>1){
            mid = left + (right-left)/2;
            if(dt.get(mid) <= target) left=mid;
            else right=mid;
        }
        return left;
    }
    private static <T>void fill(T[][] ob, T res){for(int i=0;i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(boolean[][] ob,boolean res){for(int i=0;i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(int[][] ob, int res){      for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(long[][] ob, long res){    for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(char[][] ob, char res){    for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(double[][] ob, double res){for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(int[][][] ob,int res){for(int i=0;i<ob.length;i++){for(int j=0;j<ob[0].length;j++){for(int k=0;k<ob[0][0].length;k++){ob[i][j][k]=res;}}}}
    private static void fill(long[][][] ob,long res){for(int i=0;i<ob.length;i++){for(int j=0;j<ob[0].length;j++){for(int k=0;k<ob[0][0].length;k++){ob[i][j][k]=res;}}}}
    private static <T>void fill(T[][][] ob,T res){for(int i=0;i<ob.length;i++){for(int j=0;j<ob[0].length;j++){for(int k=0;k<ob[0][0].length;k++){ob[i][j][k]=res;}}}}
    private static void fill_parent(int[] ob){ for(int i=0; i<ob.length; i++) ob[i]=i; }
    private static boolean same3(long a, long b, long c){
        if(a!=b) return false;
        if(b!=c) return false;
        if(c!=a) return false;
        return true;
    }
    private static boolean dif3(long a, long b, long c){
        if(a==b) return false;
        if(b==c) return false;
        if(c==a) return false;
        return true;
    }
    private static double hypotenuse(double a, double b){
        return Math.sqrt(a*a+b*b);
    }
    private static long factorial(int n) {
        long ans=1;
        for(long i=n; i>0; i--){ ans*=i; }
        return ans;
    }
    private static long facMod(int n, long mod) {
        long ans=1;
        for(long i=n; i>0; i--) ans = (ans * i) % mod;
        return ans;
    }
    private static long lcm(long m, long n){
        long ans = m/gcd(m,n);
        ans *= n;
        return ans;
    }
    private static long gcd(long m, long n) {
        if(m < n) return gcd(n, m);
        if(n == 0) return m;
        return gcd(n, m % n);
    }
    private static boolean isPrime(long a){
        if(a==1) return false;
        for(int i=2; i<=Math.sqrt(a); i++){  if(a%i == 0) return false;  }
        return true;
    }
    static long modInverse(long a, long mod) {
    /* Fermat's little theorem: a^(MOD-1) => 1
    Therefore (divide both sides by a): a^(MOD-2) => a^(-1) */
        return binpowMod(a, mod - 2, mod);
    }
    static long binpowMod(long a, long b, long mod) {
        long res = 1;
        while (b > 0) {
            if (b % 2 == 1) res = (res * a) % mod;
            a = (a * a) % mod;
            b /= 2;
        }
        return res;
    }
    private static int getDigit2(long num){
        long cf = 1;    int d=0;
        while(num >= cf){   d++;    cf = 1<<d;  }
        return d;
    }
    private static int getDigit10(long num){
        long cf = 1;    int d=0;
        while(num >= cf){   d++;    cf*=10;     }
        return d;
    }
    private static boolean isInArea(int y, int x, int h, int w){
        if(y<0) return false;
        if(x<0) return false;
        if(y>=h) return false;
        if(x>=w) return false;
        return true;
    }
    private static ArrayList<Integer> generatePrimes(int n) {
        int[] lp = new int[n + 1];
        ArrayList<Integer> pr = new ArrayList<>();
        for (int i = 2; i <= n; ++i) {
            if (lp[i] == 0) {
                lp[i] = i;
                pr.add(i);
            }
            for (int j = 0; j < pr.size() && pr.get(j) <= lp[i] && i * pr.get(j) <= n; ++j) {
                lp[i * pr.get(j)] = pr.get(j);
            }
        }
        return pr;
    }
    static long nPrMod(int n, int r, long MOD) {
        long res = 1;
        for (int i = (n - r + 1); i <= n; i++) {
            res = (res * i) % MOD;
        }
        return res;
    }
    static long nCr(int n, int r) {
        if (r > (n - r))
            r = n - r;
        long ans = 1;
        for (int i = 1; i <= r; i++) {
            ans *= n;
            ans /= i;
            n--;
        }
        return ans;
    }
    static long nCrMod(int n, int r, long MOD) {
        long rFactorial = nPrMod(r, r, MOD);
        long first = nPrMod(n, r, MOD);
        long second = binpowMod(rFactorial, MOD-2, MOD);
        return  (first * second) % MOD;
    }
    static void printBitRepr(int n) {
        StringBuilder res = new StringBuilder();
        for (int i = 0; i < 32; i++) {
            int mask = (1 << i);
            res.append((mask & n) == 0 ? "0" : "1");
        }
        out.println(res);
    }
    static String bitString(int n) {return Integer.toBinaryString(n);}
    static int setKthBitToOne(int n, int k) { return (n | (1 << k)); } // zero indexed
    static int setKthBitToZero(int n, int k) { return (n & ~(1 << k)); }
    static int invertKthBit(int n, int k) { return (n ^ (1 << k)); }
    static boolean isPowerOfTwo(int n) { return (n & (n - 1)) == 0; }
    static HashMap<Character, Integer> counts(String word) {
        HashMap<Character, Integer> counts = new HashMap<>();
        for (int i = 0; i < word.length(); i++) counts.merge(word.charAt(i), 1, Integer::sum);
        return counts;
    }
    static HashMap<Integer, Integer> counts(int[] arr) {
        HashMap<Integer, Integer> counts = new HashMap<>();
        for (int value : arr) counts.merge(value, 1, Integer::sum);
        return counts;
    }
    static HashMap<Long, Integer> counts(long[] arr) {
        HashMap<Long, Integer> counts = new HashMap<>();
        for (long l : arr) counts.merge(l, 1, Integer::sum);
        return counts;
    }
    static HashMap<Character, Integer> counts(char[] arr) {
        HashMap<Character, Integer> counts = new HashMap<>();
        for (char c : arr) counts.merge(c, 1, Integer::sum);
        return counts;
    }
    static long hash(int x, int y) {
        return x* 1_000_000_000L +y;
    }
    static final Random random = new Random();
    static void sort(int[] a) {
        int n = a.length;// shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }
    static void sort(long[] arr) {
        shuffleArray(arr);
        Arrays.sort(arr);
    }
    static void shuffleArray(long[] arr) {
        int n = arr.length;
        for(int i=0; i<n; ++i){
            long tmp = arr[i];
            int randomPos = i + random.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
    }
}
static class Tuple implements Comparable<Tuple> {
    int a;
    int b;
    int c;
    public Tuple(int a, int b) {
        this.a = a;
        this.b = b;
        this.c = 0;
    }
    public Tuple(int a, int b, int c) {
        this.a = a;
        this.b = b;
        this.c = c;
    }
    public int getA() { return a; }
    public int getB() { return b; }
    public int getC() { return c; }
    public int compareTo(Tuple other) {
        if (this.a == other.a) {
            if (this.b == other.b) return Long.compare(this.c, other.c);
            return Long.compare(this.b, other.b);
        }
        return Long.compare(this.a, other.a);
    }
    @Override
    public int hashCode() { return Arrays.deepHashCode(new Integer[]{a, b, c}); }
    @Override
    public boolean equals(Object o) {
        if (!(o instanceof Tuple)) return false;
        Tuple pairo = (Tuple) o;
        return (this.a == pairo.a && this.b == pairo.b && this.c == pairo.c);
    }
    @Override
    public String toString() { return String.format("(%d %d %d)  ", this.a, this.b, this.c); }
}
private static int abs(int a){  return (a>=0) ? a: -a;  }
private static int min(int... ins){ int min = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] < min) min = ins[i]; } return min; }
private static int max(int... ins){ int max = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] > max) max = ins[i]; } return max; }
private static int sum(int... ins){ int total = 0; for (int v : ins) { total += v; } return total; }
private static long abs(long a){    return (a>=0) ? a: -a;  }
private static long min(long... ins){ long min = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] < min) min = ins[i]; } return min; }
private static long max(long... ins){ long max = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] > max) max = ins[i]; } return max; }
private static long sum(long... ins){ long total = 0; for (long v : ins) { total += v; } return total; }
private static double abs(double a){    return (a>=0) ? a: -a;  }
private static double min(double... ins){ double min = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] < min) min = ins[i]; } return min; }
private static double max(double... ins){ double max = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] > max) max = ins[i]; } return max; }
private static double sum(double... ins){ double total = 0; for (double v : ins) { total += v; } return total; }

}